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Article Abstract
The inherent irreversibility of quantum dynamics for open systems poses a significant barrier to the inversion of unknown quantum processes. To tackle this challenge, we propose the framework of virtual combs that exploits the unknown process iteratively with additional classical postprocessing to simulate the process inverse. Notably, we demonstrate that an n-slot virtual comb can exactly reverse a depolarizing channel with one unknown noise parameter out of n+1 potential candidates, and a 1-slot virtual comb can exactly reverse an arbitrary pair of quantum channels. We further explore the approximate inversion of an unknown channel within a given channel set. A worst-case error decay of O(n^{-1}) is unveiled for depolarizing channels within a specified noise region. Moreover, we show that virtual combs can universally reverse unitary operations and investigate the trade-off between the slot number and the sampling overhead.
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